A Quantum Critical Point from Flavours on a Compact Space

We analyse a $2+1$ dimensional defect field theory on a two sphere in an external magnetic field. The theory is holographically dual to probe D5-branes in global AdS$_5\times S^5$ background. At any finite magnetic field only the confined phase of the theory is realised. There is a first order quantum phase transition, within the confined phase of theory, ending on a quantum critical point of a second order phase transition. We analyse the condensate and magnetisation of theory and construct its phase diagram. We study the critical exponents near the quantum critical point and find that the second derivatives of the free energy, with respect to the bare mass and the magnetic field, diverge with a critical exponent of $-2/3$. Next, we analyse the meson spectrum of the theory and identify a massless mode at the critical point signalling a diverging correlation length of the quantum fluctuations. We find that the derivative of the meson mass with respect to the bare mass also diverges with a critical exponent of $-2/3$. Finally, our studies of the magnetisation uncover a persistent diamagnetic response similar to that in mesoscopic systems, such as quantum dots and nano tubes.Comment: 26 pages, 16 figures, minor corrections, introduction expanded, typos fixed, format improved, updated to much the published versio

Near commuting multi-matrix models

We investigate the radial extent of the eigenvalue distribution for Yang-Mills type matrix models. We show that, a three matrix Gaussian model with complex Myers coupling, to leading order in strong coupling is described by commuting matrices whose joint eigenvalue distribution is uniform and confined to a ball of radius R=(3Pi/2g)^(1/3). We then study, perturbatively, a 3-component model with a pure commutator action and find a radial extent broadly consistent with numerical simulations.Comment: 25 pages, appendix expanded, presentation improved, updated to match the published versio

Commuting Quantum Matrix Models

We study a quantum system of $p$ commuting matrices and find that such a quantum system requires an explicit curvature dependent potential in its Lagrangian for the system to have a finite energy ground state. In contrast it is possible to avoid such curvature dependence in the Hamiltonian. We study the eigenvalue distribution for such systems in the large matrix size limit. A critical r\^ole is played by $p=4$. For $p\ge4$ the competition between eigenvalue repulsion and the attractive potential forces the eigenvalues to form a sharp spherical shell.Comment: 17 page

Quantised relativistic membranes and non-perturbative checks of gauge/gravity duality

We test the background geometry of the BFSS model using a D4-brane probe. This proves a sensitive test of the geometry and we find excellent agreement with the D4-brane predictions based on the solution of a membrane corresponding to the D4-brane propagating on this background.Comment: 7 pages, 2 figures, based on a talk, presented by D. O'C. at ISQS 25, 6-10 June, 2017, Prague, Czech Republic; to be published in Journal of Physics: Conference Serie

Membrane Matrix models and non-perturbative checks of gauge/gravity duality

We compare the bosonic and maximally supersymmetric membrane models. We find that in Hoppe regulated form the bosonic membrane is well approximated by massive Gaussian quantum matrix models. In contrast the similarly regulated supersymmetric membrane, which is equivalent to the BFSS model, has a gravity dual description. We sketch recent progress in checking gauge/gravity duality in this context.Comment: 11 pages and 4 figures. To appear in the Proceedings of the Corfu Summer Institute 2015 "School and Workshops on Elementary Particle Physics and Gravity" 1-27 September 2015 Corfu, Greec

A Computer Test of Holographic Flavour Dynamics

We perform computer simulations of the Berkooz-Douglas (BD) matrix model, holographically dual to the D0/D4-brane intersection. We generate the fundamental condensate versus bare mass curve of the theory both holographically and from simulations of the BD model. Our studies show excellent agreement of the two approaches in the deconfined phase of the theory and significant deviations in the confined phase. We argue the discrepancy in the confined phase is explained by the embedding of the D4-brane which yields stronger $\alpha'$ corrections to the condensate in this phase.Comment: 29 pages, 3 figures, updated to match the published versio

On the Phase Structure of Commuting Matrix Models

We perform a systematic study of commutative $SO(p)$ invariant matrix models with quadratic and quartic potentials in the large $N$ limit. We find that the physics of these systems depends crucially on the number of matrices with a critical r\^ole played by $p=4$. For $p\leq4$ the system undergoes a phase transition accompanied by a topology change transition. For $p> 4$ the system is always in the topologically non-trivial phase and the eigenvalue distribution is a Dirac delta function spherical shell. We verify our analytic work with Monte Carlo simulations.Comment: 37 pages, 13 figures, minor corrections, updated to match the published versio

The BFSS model on the lattice

We study the maximally supersymmetric BFSS model at finite temperature and its bosonic relative. For the bosonic model in $p+1$ dimensions, we find that it effectively reduces to a system of gauged Gaussian matrix models. The effective model captures the low temperature regime of the model including one of its two phase transitions. The mass becomes $p^{1/3}\lambda^{1/3}$ for large $p$, with $\lambda$ the 'tHooft coupling. Simulations of the bosonic-BFSS model with $p=9$ give $m=(1.965\pm .007)\lambda^{1/3}$, which is also the mass gap of the Hamiltonian. We argue that there is no `sign' problem in the maximally supersymmetric BFSS model and perform detailed simulations of several observables finding excellent agreement with AdS/CFT predictions when $1/\alpha'$ corrections are included.Comment: 23 pages, 11 figure

Magnetic Catalysis of Chiral Symmetry Breaking. A Holographic Prospective

We review a recent investigation of the effect of magnetic catalysis of mass generation in holographic Yang-Mills theories. We aim at a self-contained and pedagogical form of the review. We provide a brief field theory background and review the basics of holographic flavordynamics. The main part of the review investigates the influence of external magnetic field on holographic gauge theories dual to the D3/D5-- and D3/D7-- brane intersections. Among the observed phenomena are the spontaneous breaking of a global internal symmetry, Zeeman splitting of the energy levels and the existence of pseudo Goldstone modes. An analytic derivation of the Gell-Mann--Oaks--Renner relation for the D3/D7 set up is reviewed. In the D3/D5 case the pseudo Goldstone modes satisfy non-relativistic dispersion relation. The studies reviewed confirm the universal nature of the magnetic catalysis of mass generation.Comment: 49 pages, 11 figures, a review articl